Frequentist properties of Bayesian inequality tests

Working Paper Number: 
WP 19-10

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance).  For the corresponding single-draw experiment, we characterize the frequentist size of a certain Bayesian hypothesis test of (possibly nonlinear) inequalities.  If the null hypothesis is that the (possibly infinite-dimensional) parameter lies in a certain half-space, then the Bayesian test's size is alpha; if the null hypothesis is a subset of a half-space, then size is above alpha; and in other cases, size may be above, below, or equal to alpha.  Rejection probabilities at certain points in the parameter space are also characterized.  Two examples illustrate our results: translog cost function curvature and ordinal distribution relationships.

JEL Codes: 
C11, C12

Longhao Zhuo